Maximizing Profit: Solving Polynomial for MP3 Player Ad Expenses

[Bo_]

Homework Statement

P is profit in dollars of a particular mp3 player.

P = -76x^3 + 4830x^2 - 320000, 0 < x < 60

x is ad expense (in tens of thousands of $.) Find the smaller of two ad amounts that yield a profit of $2,500,000.



The attempt at a solution

All I can do is get this:

-76x^3 + 4830x^2 - 2,820,000 = 0

Now what do I do? I can't seem to factor. The only other way I know of is dividing by possible zeros, and I'm not feeling good about looking for the factors of 2.82 million.

 

[Dick]

I'm pretty sure it doesn't factor. Are you sure you aren't just supposed to give an approximate answer?

 

[Bo_]

I don't know but that'll have to do. There doesn't seem to be another way.

 

[matadorqk]

-boo boo-
sorry.

 

[matadorqk]

In what way does this contribute to helping the OP solve the problem on his own?

Oh my apologies...

*removes post*.

 

[Dick]

Oh my apologies...

*removes post*.

Thanks. You do get my point, right? I'm not trying to criticize your wish to help.

 

[pooface]

Yea, the best I can think of is the approximate answer as well.

I just used a brute method on my calculator to narrow it down. You may want to use a graphing calculator(available online) to see what the graph looks like at least.